Optimal regularity for the fully nonlinear thin obstacle problem

2021/12/10 by Colombo, Maria, Fernández-Real, Xavier, Ros-Oton, Xavier
#35B44 #35B65 #35J60 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.05458

Abstract

In this work we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent α_F such that u is C^1,α_F on either side of the obstacle. In order to do that, we prove the uniqueness of blow-ups at regular points, as well as an expansion for the solution there. Finally, we also prove that if the operator is rotationally invariant, then α_F≥ \frac12 and the solution is always C^1,1/2.

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